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Re: Erf funcion

• To: mathgroup at smc.vnet.net
• Subject: [mg123948] Re: Erf funcion
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 2 Jan 2012 02:43:30 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jdp256$rqi$1@smc.vnet.net>

I'd like to link to the same question asked earlier here:

http://stackoverflow.com/questions/8523505/using-alternative-special-functions-in-simplify-and-expand

There is one (partial?) answer there.

Vicent mentioned there that he would like to get expressions in terms of 
FiX, while keeping the definition FiX[x_] := ...   I believe this is not 
possible (except perhaps through some formatting tricks with Defer/HoldForm)

On 2012.01.01. 8:31, Vicent wrote:
 > Hello.
 >
 > I have an expression that depends on the Cumulative Distribution
 > Function (CDF) of a Normal Variable with mean = 0 and standard
 > deviation = 1.
 >
 > When I perform operations and/or derivatives with/for that function
 > with Mathematica, I get expressions involving Erf function, as the CDF
 > function of a Normal distributed variable and Erf (error function) are
 > closely related. Concretely,
 >
 >      FiX[x] == (1/2)*(1 + Erf[x/Sqrt[2]])
 >
 > and thus
 >
 >      Erf[x] == 2*FiX[x*Sqrt[2]] - 1
 >
 > where FiX stands for the previously mentioned CDF, I mean:
 >
 >      X = NormalDistribution[0, 1]
 >      FiX[x_] := CDF[X, x]
 >
 >
 > Is there a quick way to ask Mathematica not to use  Erf  but always
 > let the results as a function of FI[x]??
 >
 > The expressions I get as a result of my computations are larger than
 > this short example:
 >
 >      3 (2^(7/2 - 2 (k + t))) Cp (  E^(-d^2 - (36 Cp^2)/lambda^2))
 > ((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] + Erf[(6 Cp + d lambda)/(Sqrt[2]
 > lambda)])^k)
 >
 > where "Cp", "k", "t", "d" and "lambda" are parameters or arguments
 > that I want to keep as "generic".
 >
 > So, how can I "translate" expressions such as the last one into "FiX
 > mode"? Or, better, how can I prevent Mathematica to reduce everything
 > to "Erf mode"??
 >
 > I hope my question is clear enough... :)
 >
 > Thank you very much in advance for your answers.
 >
 > And have a good new year!
 >
 >


-- 
Szabolcs Horvát
Mma QA site proposal: http://area51.stackexchange.com/proposals/37304